Mathematics 4024 · O Level · Sketching curves

Sketching curves — practice question

This table is based on $y=x^3-3x-1$.
(a)[1]

Fill in the table.

(b)[3]

Using the grid, sketch the graph of $y=x^3-3x-1$.

(c)[2]

Use the graph to determine the roots of $x^3-3x-1=0$.

(d)[2]

Use the graph to estimate the gradient of the curve at $x=-1.5$.

(e(i))[1]

Using the grid, draw the graph of $y=4x+3$.

(e(ii))[2]

The line $y=4x+3$ and the curve $y=x^3-3x-1$ may be used to solve the equation $x^3=ax+b$. Find the values of $a$ and $b$.

(e(iii))[1]

Use the graph to find one of the negative roots of $x^3=ax+b$.

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